One-dimensional wave solutions in geophysical models of compaction

Analytical methods are used to study a class of wave solutions of compaction equations. One-dimensional wave equations are reduced to a dynamical system that allows qualitative analysis. The approach proposed makes it possible to solve the problems of existence, uniqueness, and completeness in the class of wave solutions. The trajectories of phase portraits are compared with the solutions of specific geophysical problems. The main applications of compaction mechanics in scientific publications are associated with the problems of dynamics of partially molten rocks in the Earth’s bowels; however, in recent years it has attracted the interest from other scientific and technological areas, in particular, from the oil-and-gas geophysics sector. Large volcanic eruptions are considered as an application.